Could the wielders of knives or explosive backpacks be stopped more
quickly by a single officer?
A police officer trained to deal with wielders of knives, like those in the London police force, can be quite effective at disarming or preventing further harm by stalling a wielder of a knife before further fatalities are caused, at least until armed backup arrives (which means less than ten minutes in a densely populated urban area like London). So, having an unarmed officer in that situation is not necessarily a total loss. A police baton and training and a canister of Mace could easily be sufficient to mitigate most harm from delay in access to police with firearms in a densely populated urban area.
Firearms have very limited effectiveness against people with explosive backpacks. There are many places like Afghanistan, Iraq, Pakistan, Syria and Nigeria, where explosive backpacks have been used regularly in the last several years, and in Israel, where explosive backpacks were used regularly for many years, where defenders with automatic weapons are almost ubiquitous. At best, a firearm can be used to force a suicide bomber to prematurely detonate explosives which can reduce the number of people harmed but rarely entirely prevents a deadly attack. More often, the explosives carried by a suicide bomber aren't discovered until it is too late to meaningfully mitigate harm at all.
Firearms can mitigate the harm caused with out of control vehicles (e.g., two recent cases in London, one in Nice, and one somewhere in Germany IIRC), by preventing the continued controlled use of vehicles as a weapon, but there is a narrow window of time to do so: (1) the time elapsed before it is possible to learn that the vehicle is out of control and the time when it starts to cause harm is usually a matter of seconds so eliminating all harm is virtually impossible, and (2) it is rare for the vehicle based mauling to last more than a few minutes at most before stopping anyway, with much of the harm often being caused early on, so there are limits to the benefits of firearms to stopping out of control vehicles.
The biggest benefit to having police officers universally armed with firearms, in terms of preventing mortality, is probably their ability to stop "active shooters" much more effectively than an unarmed police officer, for example, in a case like the Paris nightclub attack. An "active shooter" can do immense harm in a very short marginal period of time, and an unarmed officer can do little to stop them without grave risk of simply becoming another casualty. There are numerous instances of police and private security stopping active shooters in the U.S. who might have caused more deaths if they could continue. In some instances, a quick draw by an officer can even prevent innocent casualties.
The upshot of this is that the usefulness of universally armed police is significantly a function of the probable threats that the force will face. The more likely it is that the threat will be someone armed with a firearm, the more benefit there is to having universally armed police. The less likely it is that a police officer will encounter an armed threat, the less benefit there is likely to be to arming the police.
Would this lead to more innocent parties being killed, or could it
save lives? What are the professional arguments for and against?
Downsides to a universally armed police force:
In places where guns are very hard to gain access to (such as Japan and Great Britain), one of the important ways criminals gain access to guns is by seizing them or stealing them from police officers. For example, you don't necessarily want a prison guard patrolling the halls in a prison where inmates can come close enough to touch him to be carrying a firearm. You want to leave the firearms in those cases to guards who are in places where they aren't interacting directly with inmates (e.g. guards in guard towers rather than guards on an exercise field).
A police officer with a firearm is likely to make different choices about how to handle a volatile situation than a police officer who does not have a firearm. For example, faced with someone with a knife who is mentally ill or on drugs or a brawling person who poses a risk of using non-deadly force, a police officer with a firearm is much more likely to shoot and kill the knife or non-deadly fore wielder than a police officer without a firearm who is more prone to retreat and focus on defusing the situation. Similarly, a police officer without a firearm is likely to be far less tempted to try to kill a fleeing perpetrator who committed a non-capital crime.
A reduced likelihood of unnecessary police shootings (of both innocent and non-innocent people who are shot) can make it more likely for people to trust police which can make it easier for police to do their jobs with public cooperation which can often outweigh the benefits of having access to a firearm. Minority populations in the community that trust the police and provide them with tips are frequently the most powerful possible tool to prevent terrorist attacks as opposed to merely mitigating harm once terrorist attacks are begun.
People who commit violent crimes may be more likely to arm themselves with firearms or other comparably dangerous weapons if police are likely to be armed than if police are unlikely to be armed.
A certain small percentage of people who routinely have access to firearms commit suicide with those firearms or harm themselves or others through firearms accidents, and the amount of harm by these means is roughly proportional to the number of people who routinely have access to firearms. These harms are reduced both by having fewer officers with routine access to firearms, and by causing the few officers with routine access to firearms to be better trained to use firearms on average and more carefully supervised on average.
Again, an important part of the calculus hinges on the threat matrix faced by police officers. Some of the downsides (like theft of police firearms and an "arms race" with criminals) are the biggest concerns in places where firearm ownership rates among the general public and even more importantly the rates at which criminals have access to firearms are very low. Also, the concerns about suicide, accidental harm, and wrongful escalation due to the availability of firearms, while real and quantifiable, aren't huge. So, those concerns are only overwhelmed if the benefits from having universally armed police (which is primarily gaining an advantage against armed criminals) are pretty low - something that varies from place to place.
The bottom line is that while it makes sense for law enforcement to be unarmed in places where criminal access to firearms is extreme low (e.g. Japan and Great Britain), it makes considerably less sense when criminal access to firearms is commonplace (e.g. the U.S. and Mexico).